Hi vince. For future reference, all Shimano components are marked in inconspicuace (spelling?) places with a model number. Your 105's model is molded into the body under the hood boot. Peel that rubber boot back and you should easily find it with a flashlight and a magnifying glass.
In '09, I am thinking that 105 was still 9 spd. I'm probably wrong because my wife keeps repeating "10", "10". Do you see ST-5700 under there?
nfmisso gave you great advice regarding the cables (inners). Totally disconnect Everything from the rear brake and drlr and get the cables out of the picture. Flush it all out with that Clean Streak (great stuff!) and douse it with a thin lube (Tri-Flow is my fave). Run it through the paces (several times) and see if it performs correctly. If it does, problem solved.
You mentioned that you managed to correct the Shifting problem. Do you still feel resistance upon Braking? That may narrow it down to a Housing problem. Any deformity of a ferrule can 'choke' a cable and cause sluggish or even non-existant response. While you have the inners out - inspect those. Crashes can do wierd things.
On 105 brifters, the Main Brake Pivot Pin is totally isolated from anything that pertains to shifting. It's possible that this pin was bent in your mishap. Forcing it back to finish the ride may have compounded the problem. That is why I always recommend that Controls are tightened only enough to do what I demand of them but Move if forced.